Inverse Methods for Missing Data Imputation

Hao Wang, zhengnan li, Zhichao Chen, Xu Chen, Shuting He, Guangyi Liu, Haoxuan Li, Zhouchen Lin

Xiaohongshu· Peking University· Renmin University of China· Shanghai University of Finance and Economics· Zhejiang University· Pazhou Laboratory

missing data imputation missing data completion kernel ridge regression non-missing feature

⋅ NeurIPS ⋅ OpenReview ⋅Code

Abstract

Iterative imputation is a prevalent method for completing missing data, which involves iteratively imputing each feature by treating it as a target variable and predicting its missing values using the remaining features.

However, existing iterative imputation methods exhibit two critical defects:

model misspecification, where a uniform parametric form of model is applied across different features, conflicting with heterogeneous data generation processes;
underuse of oracle features, where all features are treated as potentially missing, neglecting the valuable information in fully observed features.

In this work, we propose kernel point imputation (KPI), a bi-level optimization framework designed to address these issues.

The inner-level optimization optimizes the model form for each feature in a reproducing kernel Hilbert space, mitigating model misspecification. The outer-level optimization leverages oracle features as supervision signals to refine imputations.

Extensive experiments on real-world datasets demonstrate that KPI consistently outperforms state-of-the-art imputation methods. Code is available at https://github.com/FMLYD/kpi.git.